Sinead O'Connor Weds in Las Vegas

Just as she'd planned, Sinead O'Connor tied the knot Thursday (her 45th birthday) with fiancé Barry Herridge. But the singer said "I do" in quite the non-traditional fashion – while sitting in the back of a pink Cadillac.

"She wanted to do the whole thing in a Cadillac. That was her thing," a source tells PEOPLE.

Arriving around 7 p.m. in a pink, low-cut dress that revealed her tattoos, the "Nothing Compares 2 U" singer filled out paperwork before settling into the Caddy at A Little White Wedding Chapel on the famous Las Vegas Strip.

"It wasn't a traditional dress, but it wasn't a traditional wedding either," says the source. "She cried during the vows and had to wipe her eyes."

After the ten minute ceremony, O'Connor and her new husband – who donned a dark jacket and pink shirt – lit candles as employees of the chapel sang "Happy Birthday" to the bride.